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I have done some "restricted" God's algorithm calculations for solving two layers of Rubik's Cube, given that the four edges of the face layer are already solved. I say it's a "restricted" calculation because it only considers certain moves or sequences of moves. For convenience, I will consider the two layers to be solved are the bottom layer (generally referred to as the D layer), and the layer above that (typically referred to by speedcubers as the E layer).

Given that four edges of the D layer are taken to be solved, the remaining four edges being considered (those that belong in the E layer) must be distributed among 8 possible edge locations. So the number of configurations for those four edges is 8*7*6*5*(2⁴) = 26880 (including orientations). The four corner cubies being considered (those that belong in the D layer) have 8*7*6*5*(3⁴) = 136080 configurations (including orientations). This makes for a total of 26880*136080 = 3,657,830,400 configurations.